Question

What is the Point of tangency in a circle?

Answer 1

Hint: A line that touches the circle at a single point is known as a tangent to a circle. The point where the tangent meets the circle is called the point of tangency. The tangent is perpendicular to the radius of the circle, with which it intersects. Tangent can be considered for any curved shape. Since tangent is a line, hence it also has its equation.

Complete answer:
Tangent to a circle is the line that touches the circle at only one point. There can be only one tangent at a point in a circle. Point of tangency is the point at which tangent meets the circle. Now, let’s prove the tangent and radius of the circle are perpendicular to each other at the point of contact.

Consider a circle in the above figure whose centre is O. AB is the tangent to a circle through point C.
Take a point $D$ on a tangent AB other than C and join OD. Point D should lie outside the circle because; if point D lies inside, then AB will be a secant to the circle and it will not be a tangent.
Therefore, OD will be greater than the radius of circle OC. This happens for every point on AB except the point of contact C.
It can be concluded that OC is the shortest distance between the centre of circle O and tangent AB.
Since, the shortest distance between a point and a line is the perpendicular distance between them,
OC is perpendicular to AB.
From the above discussion, it can be concluded that:
The tangent touches the circle at only one point
We can call the line containing the radius through the point of contact as ‘normal’ to the circle at the point

Note: The tangent to a circle is a special case of the secant when the two endpoints of its corresponding chord coincide. The tangent is considered only when it touches a curve at a single point or else it is said to be simply a line.The tangent is perpendicular to the radius of the circle at the point of tangency.